FITTING AND ERRORS IN ORIGIN As previously reported by Drs Woda and Jenkinson, the fitting section in Origin 4 is faulty. Dr Woda has sent me his data which I have refitted in three different ways with my own program, CVFIT. (1) A weighted least squares fit, using the supplied standard deviations to calculate weights as 1/(s^2), gives the same estimates as found by Dr Woda, and as given by Origin 3 and 3.5 when the "instrumental weighting" option is specified. An equally weighted (=unweighted) fit gives somewhat different estimates, as would be expected. The approximate standard deviations of these parameters can be estimated in two different ways, from the expected information matrix (which I think is what Origin uses), or from the observed information matrix (which is what I use -it is theoretically preferable, but rarely much different in practice). For each of these methods the size of the basic experimental errors can be found either (a) from the specified standard deviations, or (b) from the residuals (deviations of the observed points from the fitted lines). My standard deviations using error information from weights are similar to those given by Origin 3.5, but Origin 4.1 is clearly using the weights for the fitting process but taking the error from residuals: it is not ignoring the weights -it uses them for fitting but not for error estimation. There is nothing wrong with this procedure as long as you know what is going on, but the unannounced change between one version and another has certainly caused some confusion. It is an overstatement to say (see Scott Bertrand’s contribution) have no meaning if "instrumental weighting" is used in version 4.1. I was forced to spend time writing CVFIT because none of the commercial programs (a) stated clearly what they were doing, or (b) could be relied upon to do what they say they are doing. It seems that this is still a problem!. The language in which the fitting process is described in the manuals is particularly baffling. The fitting process is a problem in statistics, but many of the terms used are either unfamiliar or imprecise to statisticians. A weighted least squares fit, the standard description, is called a "minimum chi-squared fit with instrumental weighting", and it took me days to discover what "dependency" meant in proper statistical terms. Where does this curious vocabulary come from? I do feel that the program itself, and the description of the program, need some professional attention. David Colquhoun University College London.
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Curve fitting and errors in Origin: what it really does
Posted - 08/14/1998 : 7:38:00 PM
